Once the mistake was identified, the market bounced back, regaining about two-thirds of the sharp drop.

But the situation in Greece remains a drag on the stock market. Business leaders in San Jose expressed concern that a weaker European economy will hurt U.S. exports.

"If that economy weakens, then our exports from the United States to those countries get more expensive, so the corporations in the United States might see eroding margins and reduced profits because with our stronger currency, it becomes more expensive for those economies to purchase our goods," Wells Fargo Vice President Rob Fernandez said.

Whether it's Greece or a trading error, analysts say it shows a lack of confidence in the economy. And if consumers lack confidence, it could impact spending and the recovery.

"If it's a quick bounce and confidence resumes, then it won't be much of an impact. But in fact if the market stays down for an extended period, then sure, it would have an impact on consumer confidence and on consumer spending," Sean Randolph, Ph.D. from the Bay Area Economic Council said.

So, was there a trading glitch? While we wait for investigators to figure that out, it's interesting to note that the Nasdaq has now cancelled many trades that occurred during that chaotic 20 minutes when the markets plunged. The New York Exchange, though, insists Thursday was no error, and is not cancelling any of its trades.